Exams › IBPS PO › Quantitative Aptitude

In how many days will Raju alone complete the work? I. Aman alone can do the work in 20 days. Raju is 10% more efficient than Aman and Naina. II. Aman and Raju together can finish the work in 8\(\tfrac{2}{3}\) days, Raju and Naina in 7 days, and Naina and Aman can do the same work in 6\(\tfrac{2}{3}\) days.

1. If the data given in statement I alone are sufficient to answer the question whereas the data given in statement II alone are not sufficient to answer the question.
2. If the data given in statement II alone are sufficient to answer the question whereas the data given in statement I alone are not sufficient to answer the question.
3. If the data in either statement I alone or in statement II alone are sufficient to answer the question
4. If the data in both the statements I and II are not sufficient to answer the question.

Correct answer: If the data given in statement II alone are sufficient to answer the question whereas the data given in statement I alone are not sufficient to answer the question.

Solution

Statement I is insufficient because knowing Aman’s time and that Raju is 10% more efficient than Aman and Naina does not uniquely determine Raju’s time. Statement II gives three pairwise work-rate equations, which are enough to solve for each person's rate individually. Therefore, statement II alone is sufficient.

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